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Generalized forgetting functions for on‐line least‐squares identification of time‐varying systems
Author(s) -
Mahony R. E.,
Lozano R.
Publication year - 2001
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.630
Subject(s) - lyapunov function , parametric statistics , least squares function approximation , convergence (economics) , mathematics , representation (politics) , identification (biology) , control theory (sociology) , function (biology) , minification , forgetting , system identification , mathematical optimization , computer science , nonlinear system , statistics , artificial intelligence , data modeling , philosophy , database , estimator , law , linguistics , biology , control (management) , quantum mechanics , evolutionary biology , political science , physics , botany , politics , economics , economic growth
The problem of on‐line identification of a parametric model for continuous‐time, time‐varying systems is considered via the minimization of a least‐squares criterion with a forgetting function. The proposed forgetting function depends on two time‐varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time‐varying error terms in the parametric model representation. Copyright © 2001 John Wiley & Sons, Ltd.